Symmetries of asymptotically flat axisymmetric space-times with null dust

Symmetries of space-times with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in an axially symmetric space-time with null dust field in which at least locally a smooth null infinity in the sense of Penrose exists, the only allowable additional Killing vector forming with the axial one a two-dimensional Lie algebra (the axial and the additional Killing vector are not assumed to be hypersurface orthogonal) is a supertranslational Killing vector and the gravitational field is then nonradiative (the Weyl tensor has a nonradiative character). (C) 2000 American Institute of Physics. [S0022-2488(00)06605-6].